Richard III(1955) [Lady Anne]: Killed (off-screen) by Laurence Olivier. Her body is not shown; we only learn of her death when Laurence mentions it in one of his monologues. She later appears as a ghost or hallucination when Laurence has a vision of several of his victims appearing to him.

Romeo and Juliet (1955) [Juliet]: Commits suicide by stabbing herself in the chest.

Anna Karenina (1961) [Anna Karenina]: Commits suicide by throwing herself under the wheels of a train.

The Illustrated Man(1969) [Felicia]: Mauled to death (off-screen), along with Rod Steiger, by a computer-generated lion inside a "hologram" room. We only hear them screaming as we see the lion attack; her body is not shown afterwards.

Henry VIII(1979) [Katherine of Aragon]: Presumably dies of cancer. (I haven't seen this version, so I don't know whether it covers her death.) (Thanks to PortsGuy)

Hamlet, Prince of Denmark (1980) [Queen Gertrude]: Poisoned when she drinks from the cup which Patrick Stewart had intended for Derek Jacobi.

The Life and Death of King John(1984) [Constance]: Dies off-screen (I don't know the cause of death). (I haven't seen this version, but I've read a broad outline of Shakespeare's play, which includes a scene of a messenger bringing news of her death.)

The Theban Plays: Oedipus the King (1984) [Jocasta]: Commits suicide by hanging herself after discovering that she's unwittingly married her own son. (Thanks to Gordon)

Anastasia: The Mystery of Anna (1986) [Czarina Alexandra]: Executed, along with the rest of the royal family, by a firing squad of Bolsheviks.

The Mirror Crack'd (The Mirror Crack'd from Side to Side) (1992) [Marina Gregg]: Poisoned, presumably by Barry Newman. (The 1980 version with Elizabeth Taylor presents the death as a suicide, but this version implies that it's murder.) (Thanks to Daniel)

Daylight(1996) [Eleanor Trilling]: Dies of hypothermia while trapped in the tunnel. (Thanks to Eugene)

Shakespeare's Women & Claire Bloom (1999) [Herself]: I haven't seen this documentary on her career, but it seems pretty likely that it might contain footage of some of her death scenes from various Shakespearean adaptations.